DEPENDENCE OF THE INPUT IMPEDANCE OF ATHREE-ELECTRODE VACUUM TUBE UPON THELOAD IN THE PLATE CIRCUIT

By John M. Miller

CONTENTSPage

I. Introduction 367

II. General theory of the dependence of the input impedance upon the

load in the plate circuit 369

III. Input impedance for the case of a pure resistance load in the plate

circuit 373

IV. Experimental determinations with 3 pure resistance load in the plate

circuit 375

1

.

Determination of k, r^ and p .

^- 375

2. Determination of Ci, C2, and C3 375

3. Determination of Cg 377

4. Comparison of observed and computed results 377

V. Input impedance for the case of an inductive load in the plate circuit.

.

379VI. Experimental determinations with an inductive load 383

1

.

Determination of the tube constants 3832. Measurement of the oscillatory circuit resistance 384

3. Comparison of observed and computed results 384

VII. Input impedance for the case of a capacity load in the plate circuit 385VIII. Stmimary of results 385

1. INTRODUCTION

In a previous paper * was treated the theory of the use of a

three-electrode vacutun tube as an amplifier, showing the impor-

tance of the amplification constant as determining the voltage

amplification of the tube and the internal resistance of the tube

in the plate or output circuit as determining the alternating

current flowing in that circuit. A dynamic method was given for

determining these important quantities directly.

The present paper is an extension of the theory and is con-

cerned with the characteristics of the grid or input circuit. Theinput impedance of the tube is of importance in determining the

input power and the voltage supplied to the input terminals of

the tube by the apparatus in the input circuit.

1 Miller, Proc. I. R. E., 6, 141; t^8.367

368 Scientific Papers of the Bureau of Standards [voi.15

If the grid of the tube is positive with respect to the filament,

there will be a flow of electrons between the filament and grid. If

distortion is neglected and the frequency is so low that capacity

effects are negligible, the internal input circuit is under these

conditions characterized by a pure resistance and an emf in.

series. The value of the resistance is determined by the reciprocal

of the slope of the grid-current—grid-voltage characteristic cor-

responding to the operating voltages. This is analagous to the

internal or output resistance of the plate circuit. The internal

emf which acts in the grid circuit is determined by the product of

the ratio of the slopes of the grid-current—plate-voltage and

grid-current—grid-voltage characteristics with the alternating

voltage of the plate relative to the filament which occurs as the

result of a load in the plate circuit. This again is analagous to

the way in which the amplification constant and impressed alter-

nating voltage on the grid determine the voltage acting in the

plate circuit of the tube. All of these facts are implicitly con-

tained in the equations (5) derived by M. Latour ^ in his paper on

the "Theoretical Discussion of the Audion."

If the grid of the tube is negative with respect to the filament

so that no appreciable electron flow takes place between these

electrodes, it would appear offhand that the input impedance of

the tube would be rather unimportant in determining the voltage

received from the apparatus in the external circuit. In very

many cases in practice, however, this is not true, and as a conse-

quence of the capacities between the tube electrodes and con-

necting wires, the internal characteristics of the plate circuit of

the tube and the external load in the plate circuit, the character

of the input impedance of the tube markedly affects its behavior

as an amplifier. The following treatment will be concerned

solely with the character of the input impedance of the tube whenthe grid is negative with respect to the filament.

It will be shown that when the load in the plate circuit is a

resistance or capacity the input impedance can be represented

as a positive resistance and capacity in series. Thus the tube is

not a pure voltage device, but absorbs power.

When the load is inductive the input impedance can, in manycases, be represented as a negative resistance and capacity in

series. This represents regeneration through the tube itself, and

is of importance in the regenerative effects and oscillations in

amplifiers.

»M. Latour, "Electrician," 78, p. 280; 1916.

MUler] Input Impedance of Vacuum Tube 369

n. GENERAL THEORY OF THE DEPENDENCE OF THEINPUT IMPEDANCE UPON THE LOAD IN THE PLATECIRCUIT

A three-electrode vacumri tube and associated circuits may be

represented diagrammatically as in Fig. i, where the continuous

lines represent the circuits outside of the tube, while the dotted

lines show the internal electrical characteristics of the tube. The

points F, G, and P represent the three electrodes, filament, grid^

and plate. The filament, grid, and plate batteries are not shown.

Between filament and grid in the external circuit is applied the

input emf which is an alternating voltage Eg. In the external

circuit between filament and plate is inserted apparatus, such as

phones, or the primary winding of a transformer, and this is

designated in the figure as any impedance Zp =Rp + jXp where

Zf<

Fig. I.

—

Diagramatic representation of a vacuum tube and external circuits

i?p is the resistance component and Xp the reactance component.

The latter may be positive or negative, according as to whether

it is inductive or capacitive. Within the tube the capacities

between the three electrodes are represented by Ci, C^, and C3.

In general, the capacities between the leads to these elements are

not negligible and will be assumed to be lumped in correct mannerwith the intraelectrode capacities. Further, as shown in the

earlier paper cited above, the impressed emf Eg gives rise to an

internal emf k E^ {k = amplification constant) which, acting in

series with the internal output resistance rp, is impressed between

the filament and plate of the tube. In this diagrammatic repre-

sentation of the tube it is assumed for simplicity that the capacities

between the tube electrodes and appropriate leads are free from

dielectric absorption and that the grid is maintained sufficiently

negative with respect to the filament, and the insulation andvacuimi are such that there is no appreciable conductive flow

370 Scientific Papers of the Bureau of Standards- [Vol. IS

between the grid and filament as a result of the impressed emf Eg,

Otherwise it would be necessary to assume resistances in series or

in parallel with the capacities C^, C^, and Cg to represent dielectric

losses and an emf and series resistance in parallel with Q, as dis-

cussed above.

The problem, then, of finding the input impedance of the tube

Zg is that of determining the current Ig which flows in the external

input circuit as a result of the voltage Eg. In Fig. 2 the circuit

is redrawn and the ctirrents represented as Ig, I^, 12, /g, etc.

Fig. 2.

—

Vacuum tube and external circuits as an electrical network

By Kirchhoff's laws we have the following seven equations

connecting the seven unknown cturents, which permit us to deter-

mine Ig in terms of the quantities Eg, k, Zp, rp, Q, C2, and C3.

Thus,

k Eg=lQ rp+ZgZp

Ic=I. +h

(I)

(2)

I,

h

Eg = .jo)C^

(3)

(4)

(5)

(6)

(7)

Eliminating /j, I^y Is, h, h, and I^ between these equations and

Miuer] Input Impedauce of Vacuum Tube 371

writing 2?^ = -^we obtain the following expression for the input

impedance

:

.. = ;'^-^^

(8)

k C2 + Ci4-C2 + ^(Ci +Q +y w rp (Q Q +Q Cg+Q C3)Z,p

Substituting Zp = i^p + / Xp (9)

in (8) we obtain the equationa+jb , V

where

i?p I

6 = Xp(C, + C3)-^^^

c =^ (ib C2 +C1+Q +Ci + C2-a) Xp (C, C^ +Q C3+ C, C3)

(/ =^ (^C^ + Ci + CJ+coi^p (C1C2 + C1C3 + C2C3)^p

And if Zg is separated into resistance and reactance components

Yg and Xg, we have

Ze=rii+jXg (12)

(13)a c + b d

'firc^ + d^

bc-ad

If Xp is negative, corresponding to a capacity reactance in the

plate circuit, we have the following terms in the numerator of Vg :

Positive terms Negative terms

c^X^^{C, + C,) iC,C, + C,C, + C,C,)^ wXpi?p (C2 + C3) (CA +^ 1^ 3 I" ^ 2^ 3/

^ (C, + C3) (fee,+ C. + C) ^ (CA+ c,c, +CA)

^(feC, +C.+Q ^(feC, +C.+Q

372 Scientific Papers of the Bureau of Standards [Voi. 15

Positive terms Negative terms

^ {C,+ C,) (feC, +C,+Q ^ (CA + C.C3 +CA)/p /p

It is evident from inspection that the positive terms will exceed

numerically the negative terms when Xp^o, and since the denom-inator of rg is always positive, r^ must always be positive.

The resistance component of the input impedance of a three-

electrode vacuum tube is always positive, and hence the input

absorbs power if the load in the plate circuit is capacitive or a pure

resistance even when the grid is negative with respect to the fil-

ament.

In the succeeding treatment it will be shown that the input im-

pedance of the tube may be equivalent to a considerable capacity

with a high resistance in series, in which case the absorption of

power in the input of the tube becomes very large.

If, however, the load is inductive (Xp>o), the terms above

which contain Xp will change sign. The munerator of r^ will then

become

i?pC,^ +^ ikC,' + C,' + kC,C,) +^ (kC^ + C,' + kC,C,) -^ (kC,) .

rp r-p o)rp

Hence r^ will be negative if

^p>^p! ^kC, + C,+ kC,)+^ (kC, + C, + kC,) +RpC,. (15)Cy/

p

/ p / p

The resistance component of the input impedance of a three-

electrode vacuum tube can be negative and the tube will supply

power to the external input circuit; i. e., regenerate, if the load in

the plate circuit is inductive.

This explains the regenerative effect of an inductive load pre-

viously noted by Armstrong,^ and also the regenerative effects and

oscillations in amplifiers, which can occur even when there is no

electrostatic or electromagnetic coupling between the input and

output circuits other than through the tube itself.

The dependence of the regenerative action upon the inductive

load in the plate circuit will be treated theoretically and experi-

mentally in a succeeding section.

' Armstrong, E. H., Proc. I. R. E., 3, p. 215, 1915; in particular Fig. 10, on p. 220.

Mmer] Input Impedance of Vacuum Tube 373

III. INPUT IMPEDANCE FOR THE CASE OF A PURE RESIST-ANCE LOAD IN THE PLATE CIRCUIT

We will first consider the case where the load in the plate cir-

cuit is a pure resistance; that is, Zp=i^p. Equation (8) then

becomes

>-p(C, + C3)-i(.H-g)

^<f= 7

—

z-\^

(16)

kC,-{-li +^KC,+C,) +j CO i-p (Q C, + C, C3 + C2 C3)

If we let a = rp (C2 +C3)

d=rp (Ci C2+C1 C3+C2 C3)

(17)

(^'<^-^j(c-yco£f)

Then 2 - ^ ^^ _^c +M I

^"^(bc + ac^'d)

If the input impedance is represented by an apparent resistance

Tg in series with an apparent capacity Cg, the values of these

quantities are given by_a c + b

d

^^c^ + co^d^

(18)

^'"'bc + aoi^d

The relative importance of the quantities involved may be ex-

pressed by 6> > a, c > > (f . Hence at low frequencies (in gen-

eral for CO < 10^)

a c + b d

(19)

For Rp = 0; rg=0; Cg = Ci + C2. Under these conditions the plate

circuit constitutes a short circuit between filament and plate,

eliminating the capacity C3 and putting Cj and C2 in parallel be-

tween grid and filament.

136038°—19 2

374 Scientific Papers of the Bureau of Standards [Vol. IS

As Rp increases relative to rp, both r^ and Cg increase, tg canincrease to nearly the order of rp. The variation in Cg can be ex-

pressed by the equation

From this it appears that the capacity Cg between grid and fila-

ment is important in increasing the apparent input capacity.

The maximum increase (fori^p > > rp) is k C^. It is of interest

k Rto note that the quantity ——-^ is, imder the assiuned fre-

rp +/vp

quency conditions, the ratio of the voltage across R^ to the input

3.

—

Variation of input characteristics with resistance load in the plate circuit

voltage Eg and hence determines the voltage amplification per

stage of a resistance coupled ampHfier. Thus the apparent input

capacity can become a number of times greater than the actual

capacities between the tube electrodes, and since the apparent

input resistance can also become very high, the dissipation of

power in the input circuit of the tube may be considerable, even

when the grid is negative with respect to the filament.

When the frequency is so high that the terms containing w^ be-

come important, these resistance and capacity effects become less

marked. For very high frequencies

rg=0

This latter is the capacity of C2 and C3 in series and paralleled

MiUer] Input Impedance of Vacuum Tube 375

by Cj—^i. e., the capacity between filament and grid with the

plate circuit open. At these frequencies, however, the voltage

across the resistance R^ is reduced, because of capacity effects

and approaches zero with increasing frequency. Fig. 3 shows

the variation of r^ and Cg with the load R^ for a particular tube of

the J or VT-i type for wave lengths longer than about 2000 m.

IV. EXPERIMENTAL DETERMINATIONS WITH A PURE RE-SISTANCE LOAD IN THE PLATE CIRCUIT

1. DETERMINATION OF i, r- AND

A dynamic method for determining k and rp, which was de-

scribed in an earlier paper,^ was utilized in these measurements.

Since with a constant plate battery the actual voltage on the tube

is reduced as a result of the drop in voltage across R^, the deter

-

kRminations were so made that values of k,r^, and ^ .

^ could be/Vp + Tp

obtained which corresponded to the actual voltage on the plate

for a given i?p. This was effected by obtaining curves for k and

fp for varying plate voltages, and then, v/ith a constant plate

battery, the actual voltage on the tube was determined for differ-

ent values of R^ by making readings of the plate current and

computing the voltage drop.

Two of the tubes used in the experiments and the electrical

data of their use are described in Table i.

TABLE 1

Type.Plate

voltage*

Filamentcurrent

Gridvoltage

JorVT-1. 40

40

1.1

0.2

— 1.5

VT-3 —1.5

Figs. 4 and 5 give the curves showing the dependence of k, r^,

k Rand p ^ upon the load R^ for these two tubes,

/vp -r yp

2. DETERMINATION OF C^, C^, AND C3

A series-resistance capacity bridge was used to measure the tube

capacities, using an amplifier and phones as a balance indicator.

A ground connection was put on a third arm of the bridge, andthis w^as adjusted so as to bring the detecting arm of the bridge

* See reference i.

376 Scientific Papers of the Bureau of Standards [Vol, IS

at ground potential. The measurements were made at about

IGOO cycles with a few tenths of a volt impressed on the bridge.

Under these conditions the bridge was sensitive to one-tenth

/OOfiOO

Jiesisiance LooLd. in Plate Ctrcuit, Ohms.

Fig. 4.

—

Amplification constant, voltage amplification and internal plate circuit resistance

with varying resistance load. VT-I tube

micromicrofarad. One arm of the bridge contained a variable

air condenser of 250 micromicrofarads capacity, across which the

capacities to be measured were connected and determined by the

necessary change in the variable to maintain the bridge balance.

nfi*'f

% - k-

5

• */?P

4f^P*rp

^^ .

/^ rp ^ ^/>.yT- 5 Tub r

-^" ^d. t^t7«e '. •ife

^

40 aee noooo /oeooo

Heaisiance Load in Plait Circuii, Ohm^.4Sm*••

Fig. 5.

—

Amplification constant, voltage amplification and internal plate circuit resist-

ance with varying resistance load. VT-j tube

The filament, plate, and grid batteries were connected directly

to the negative filament terminal, and this point was likewise

connected to the ground potential part of the bridge. Those

MiUer] Input Impedance of Vacuum Tube 377

portions of the connecting leads to the tube electrodes which

followed the potentials of the electrodes themselves were con-

sidered as part of the electrodes and included in the capacity

measurements. The tube socket was a Signal Corps receiving-

tube socket and its capacities were also included.

The capacities Q, C2, and C3 were separately determined in

the following manner:

(a) Connect G and P together and measure capacity to F,

This short-circuits C2 and gives C^ + Cs.

(b) Connect G and F and measure to P. This gives C^ + C3.

(c) Connect F and P (i. e. i?p = 0) and measure to G. This

gives Q + C2.

From these observations, then

2C,= (a)-h(c)-(b)

2C,= (b) + (c)-(a)

2C3=(a) + (b)-(c)

The values of the capacities in micromicrofarads as measured

for the two tubes mentioned previously were found to be as shown

in Table 2.

TABLE 2

Type C1+C3 C2+C3 01+ C, Ci C2 C3

VT-1 28.2

24.1

26.6

18.8

27.9

18.9

14.7 6

12.1

13. 1»

6.8

13.4,

12.0VT-3

These capacity values are considerably increased because of

the tube socket and leads used in the experiments.

3. DETERMINATION OF c^

The apparent input capacity Cg for different resistance loads wasdetermined in the same way as Ci+Cj in (2) above, excepting

that the resistance R^ was inserted in the plate circuit of the tube.

4. COMPARISON OF OBSERVED AND COMPUTED RESULTS

In Tables 3 and 4 the various resistance loads which were in-

serted in the plate circuit are given in the first column and in the

other columns the calculated and experimentally observed values

of the input capacity Cg are given in micromicrofarads.

378 Scientific Papers of the Bureau of Standards

TABLE 3.—VT-1 Tube

{Vol. 15

i2p,ohins

Input capacity

Computed Observed

8000

16 000

49 400

97 000

139 000

27.9

49.0

61.5

76.1

84.3

87.6

51.4

64.5

78.9

84.2

86.1

TABLE 4.—VT-3 Tube

Input capacity

i2p,olims

Computed Observed

18.9

8200 31.8 32.4

18 500 38.1 40.1

49 800 45.1 46.9

98 500 47.5 51.2

140 500 49.0 53.1

To show the importance of the capacity C2 in determining Cg a

separate series of measurements were carried out in which the

capacity C2 was increased by connecting a small condenser between

the grid and plate. A different tube of the VT-i type was used

in these measurements and the resistance R^ was 30 000 ohmskR,

throughout, leading to a value ofi^p + rp

of 3.29. Measurements

of the apparent input capacity were made with C2 increased byzerO; 17.5, and 34.3 micromicrofarads. The values of Cj were,

then, 1 1.8, 29.3, and 46.1 micromicrofarads, the value of Q was12.2 micromicrofarads, the values of C1+C2 were 24.0, 41.5, and

58.3 micromicrofarads. The values of Cg as calculated from the

k Rformula Cg'=C^+C2-\-C2 — p for the three cases were 62.8,

^p "T" ivp

137.9, and 210.0 micromicrofarads. The experimentally observed

values were 64.3, 138.6, and 205.4 micromicrofarads, showing an

agreement of about 2 per cent.

It was found to be impossible to check the values of r^ experi-

mentally at the frequencies used in the bridge measurements be-

cause of dielectric absorption in the tube capacities. At these low

frequencies the dielectric losses introduce effective resistances

Miller] Input Impedance of Vacuum Tube 379

which are many times greater than those given by the expression

for Yg, which does not take dielectric losses into account. Themeasurements can no doubt be made at radio frequencies, but are

rendered somewhat difficult because of the limited input voltage

which can be apphed to the tube if the grid is to remain at all

times negative with respect to the filament. The dielectric losses

in the tube capacities are doubtless important in the use of tubes

at long waves, and should be taken into account in the design of

tube bases and sockets.

V. INPUT IMPEDANCE FOR THE CASE OF AN INDUCTIVELOAD IN THE PLATE CIRCUIT

In case the load in the plate circuit is an inductance Lp and re-

sistance R^ and the input impedance of the tube is represented bya series resistance Vg and capacity Cg, we obtain from equations

(11), (13), and (14) the following:

_ a c-\-h d , .

(c' + d^)

^^~CO {ad -be)

^^^^

where

6 = coLp(C3 + C3)-j|-J (23)

c = -? (kC. + C, + C,) +C,+C,- io-^L^ {C,C, + QC3 + QC3)^P

J =^ (kC, + C, + C,) + coi^pCQQ + QC3 + C2C3)^p

As already pointed out above in expression (15), the numerator of

Yg, and hence Yg itself, will be zero or negative when

^5^ (fee, + C, + feCJ +^ (fee, + C, + feQ) + i?pC, (24)y p / p » p

The equality sign determines the values of Lp, for which the input

resistance is zero. If R^ is large, the solutions for Lp at a given

frequency may be imaginary, in which case no inductive load canmake the input resistance negative.

Curves showing the variation in the input resistance and input

capacity with the inductance in the plate circuit are given in

38o Scientific Papers of the Bureau of Standards Wol. IS

Figs. 6 and 7 for various values of Rp, These were computed,

using formulas (21), (22), and (23) for a frequency given by6) = 2Xio% and assiuning the constants k = 6, Q =C2 = C3 = io"^^

and rp = 2Xio*, which are approximately those of a VT-i tube.

If we asstune that the resistance in the plate circuit is so low

compared to the reactance of Lp that the terms containing R^are negligible, the inequality of (24) reduces to

03^Lr (c,+c,+5)<I (25)

« 4- e'CMit.Mimhmrxrvea.S .0 12. »-^

1\ s

\,\

./

A V

\,

*-.*.. .0 ^ >-^

\N ^^^

-3

-4

-5

^S^^TT ^^•

\ ^ <^/y

1 v^ "~V1 t^'///

1

\ //'^-^V/

-8 \ /\y

Fig. 6.

—

Negative input resistance caused by inductive load in plate circuit

This shows that the combination of inductive load plus the tube

capacities must still be an inductive reactance in order to have

regeneration, and determines the highest frequency with a given

inductance Lp or the highest value of Lp at a given frequency at

which regeneration can occur. At low values of Lp, or at low

frequencies where oi^Lp{C^y C2, or C3) is small compared to imity,

and assuming R^ is small compared to r^ or wLp, the only term

in the ntunerator of r^ which is of importance is ^ {kC^ . From

(21) and (23) it is seen that the denominator of r^ reduced to

(Ci + Cg)^. Hence the value of the input resistance is given by

Ln {k C)rtr= -

rp (Q +Q^ (26)

Miller] Input Impedance of Vacuum Tube 381

From (22) and (23) it can be seen that imder the above assump-

tions the input capacity is given by

Cg — L- J "T" ^ 3 (27)

Under these conditions, therefore, the input impedance of a tube

consists of a negative resistance proportional to the inductance

in the plate circuit in series with a constant capacity. This

corresponds to the portion of the curves of Figs. 6 and 7 for

Rp = and low Lp.

^.80f*^^oi\

^^ = 1*^.1.000

ft^,5/>oc

A.

\to /^^^^ ^^ Kr'iojai •A

060

4/^

y.^^

1

J^

'7i0/

<^V

c I 4 t / «*/nJ* TlfiLta Cir-ct4.it*, M.\

Fig. 7.

—

Variation in input capacity with indtutive load

The magnitude of the regenerative effect produced by the

negative input resistance will depend upon the constants of the

external input circuit. The effect will be to reduce or neutralize

the positive resistance of the external circuit. In general an

oscillatory circuit is connected to the input of the tube and the

apparent resistance of this circuit is reduced as a result of the

regenerative action. When rg and Cg are such as completely to

neutralize the resistance of that circuit, oscillations will take

place.

In the case of an amplifier this input circuit may be a trans-

former. The complete input circuit will be as shown in Fig. 8,

where L and C represent the coil and condenser of the oscillatory

382 Scientific Papers of the Bureau of Standards [Vol. 15

circuit, of which the resistance is R. The input characteristics

of the tube are represented by r^ and Cg. The reduction in the

resistance of the oscillatory circuit which results when r^ is nega-

tive, can be calculated as fol-

lows. Since the reactance of

Cg is ordinarily very large

compared to the numerical

value of rg, the current / in

the oscillatory circuit will di-

vide between C and the par-

allel branch containing Cg in

proportion to the capacities

C and Cg, Hence the current

#Fig. 8.

—

External grid circuit and input imped-

ance of tube

Ig flowing into the grid of the tube and through the resistance r^

is given by

^' ^ C + Cg(28)

The power dissipated in rg will be Pg =Ig% = ^^(-7^— ) ^g (29)

This will be negative when rg is negative, thus representing a

generation of power. The power dissipated in the resistance R is

Pn=PR (30)

and the total power

P=P3+P, = p[i? +(^)V,] (3x)

Thus when rg is negative the reduction in the circuit resistance

will be given by

AR\C + Cg)

(32)

In Fig. 9 are plotted curves of received signal against the

inductance in the plate circuit, assuming the same tube constants

and frequency as in Figs. 6 and 7, that the resistance in the plate

circuit is negligible (i?p=o) and that the capacity C of Fig. 8 is

0.0015 microfarad. Tliree curves are shown corresponding to

circuits of 7, 9, and 10 ohms resistance. The received signal is

taken to be proportional to the reciprocal of the circuit resistance

as reduced by the regenerative effect. The curves for the 7 ohmcircuit run to infinity, indicating complete neutralization of the

Miller] Input Impedance of Vacuum Tube 383

circmt resistance and hence oscillations. The curves for the 9

and 10 ohm circuits are quite similar to that given by Armstrong.*

For low values of Lp we find by substituting the values of Vg and

Cg from (26) and (27) in (32)

AR =rp iC + C,+C,) (33)

The regenerative effects are increased by increasing Lp, decreasing

C, or by connecting a condenser between grid and plate so as to

increase C^ when C2 is small compared to C.

1

1

"I\

1

1

1

\

1

1

/^ \

/

\ I

1 \ \

•5 f \ \

/ hn-\ \ \^ // / \A \

/ /// \iv \Ny ^^^

i 1V i <

Ui» ar <

rerA.it,

» 1 II I z.

Fig. 9.

—

Variation of received signal with inductive load in the plate circuit

VI. EXPERIMENTAL DETERMINATIONS WITH AN INDUC-TIVE LOAD

Expression (33) was checked by measuring at radio frequencies

the reduction in resistance of an oscillatory circuit connected to

the input terminals of the tube when different inductances of

known value were inserted in the plate circuit.

1. DETERMINATION OF THE TUBE CONSTANTS

A type J or VT-i tube was used with 40 volts on the plate,

— 1.5 on the grid, and a filament current of i.i amperes. The

» Armstrong, loc. cit.

384 Scientific Papers of the Bureau of Standards [Vol. IS

tube constants were measured, as outlined in Section IV above,

and were found to be as follows for the tube used: k = 'j.2,

^'p = 29 300, C2 = 1 2.2, and Ci + C2 = 25.7 micromicrofarads.

2. MEASUREMENT OF THE OSCILLATORY CIRCUIT RESISTANCE

The oscillatory circuit was coupled to a driving circuit, and its

resistance was measured at 900 m. wave length by the resistance

variation method. The capacity C was 1675 micromicrofarads.

The current indications were obtained with a vacuum thermocouple

of 4.8 ohms resistance and a sensitive wall galvanometer. Withthis value of the capacity and frequency sufficient measuring cur-

rent was obtained without impressing more than one volt across

the condenser or on the input of the tube. Measurements madewith the tube disconnected from the condenser C, and then con-

nected, but with no inserted inductance in the plate circuit,

showed that the dielectic losses in the tube capacities were not

appreciable at this frequency. The resistance of the oscillatory

circuit was then determined with 254 and 6S0 microhenries

inductance in the plate circuit.

3. COMPARISON OF OBSERVED AND COMPUTED RESULTS

The theoretical reduction in the circuit resistance was com-

kCputed from formula (33) ; the value of the factor—(r^r"^^'r ^2

as calculated from the tube constants and capacity C being

1.037 Xio^. The results are compared in Table 5. In the first

column are given the values of the inductive load in microhenries,

in the second column the corresponding observed circuit resist-

ances, in the third column the observed reduction in the circuit

resistance, and in the fourth column the reduction in circuit re-

sistance as computed by formula (33)

.

TABLE 5

Induct-ance, mi-crohenries

Circuitresistamce.

Reduction in circuit

resistance

ohmsObserved Computed

254

680

6.58

6.32

5.88

0.26

.70

0.26

.70

Muier] Input Impedauce of Vacuum Tube 385

VII. INPUT IMPEDANCE FOR THE CASE OF A CAPACITYLOAD IN THE PLATE CIRCUIT

The equations of the input impedance for a capacity load can

likewise be derived readily from equations (11), (13), and (14).

In this case the input resistance will always be positive, so that

the input absorbs power. Thus the presence of phones in the plate

circuit of a tube may cause a dissipation of power in the input,

because of the phones having a capacity reactance at high fre-

quencies.

VIII. SUMMARY OF RESULTS

1. Because of the capacities between the elements of a three-

electrode vacuum tube, the input impedance of the tube depends

upon the nature of the load in the plate circuit of the tube.

2. Even when the grid of the tube is negative with respect to the

filament, the input impedance can be such as to absorb consider-

able power from the input circuit, This occurs when the load in

the plate circuit is a resistance or capacity reactance.

3. When the load in the plate circuit is inductive, the input

impedance can be characterized by a negative resistance, in

which case regeneration or oscillations can occur as a result of

coupling through the tube itself.

In conclusion the author desires to express his indebtedness to

the Signal Corps, who requested and supported this investiga-

tion, and to Miss Dora E. Wells, of the Bureau of Standards, whoperformed most of the experimental work. The above results

were communicated to the Signal Corps in reports dated April 8

and April 30, 191 9, and are published with their approval.

Washington, June 11, 191 9.

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